Algebra/Probability

Probability is the chance that something will occur. For example, what are the chances that two dice rolled will equal 7? To solve this, a chart can be made of all the pairs of the integers {1, 2, 3, 4, 5, 6} that add up to 7.


 * 1 + 6
 * 2 + 5
 * 3 + 4
 * 4 + 3
 * 5 + 2
 * 6 + 1

note that the first three seem to be the same as the second three. This is because there are two dice, so when the first die gets number X and the second gets Y, it's a different outcome than the first being Y and the second X.

Next, we find out how many possibilities there are in total.

6 possibilities for the first die * 6 possibilities for the second = 36 combinations.

Since 6 out of the 36 combinations add up to 7, the answer is 1/6 or 16.6666666...% or 0.166666666... Usually, probabilities are measured in the first or second way.

Ratios
Quite often, ratios are used to show the probability of an event occurring compared to another event. Be careful! The ratio of heads to tails is 1:1 or 1/1, but the probability of heads is 1:2 or 1/2. Don't confuse these two ways of writing the same thing.